Marjorie needs to calculate how much water a cylindrical tank will hold. The tank is 9 feet high and has a diameter of 5 feet. Her work is shown below.

V = pi r squared h

Step 1: V = pi (2.5 squared) (9)
Step 2: V = pi (5) (9)
Step 3: V = (3.14) (5) (9)
Step 4: V = 141.3 cubic feet

What error did Marjorie make when calculating the volume of the tank?
In step 1, she substituted into the volume formula incorrectly.
In step 2, she calculated 2.5 squared incorrectly.
In step 3, the she substituted the wrong amount for Pi.
Marjorie correctly calculated the volume of the cylinder.

Answer: #18 is (1/2,0)

#19 (0,-1)

#20 5

#21 8√2 or 11.313708498985

Step-by-step explanation:

The first number is 11 and second number is 12.We can find by solving two consective numbers.

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed and it follows a pattern. For example 1, 2, 3 are the first three consecutive natural numbers.

An odd number of consecutive numbers has a whole number as an average. This average is always the middle number. So that means that the sum of the numbers will be Sum = average \times number of consecutive numbers.

Now we find

Let x be a first number and x+1 be a second number.So

x+x+1=23

2x+1=23

2x    =23-1

2x    =22

  x   = 11

x+1= 11+1=12

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Answer:

w = 9

m <4 = 157

m<2 = 23

Step-by-step explanation:

The measure of the arc of a straight line is 180⁰.

so angle 1 + angle 3 = 180⁰.

(3w - 4) + 157 = 180

3w = 27

w = 9

Answer:

w = 9

m 4 = 157

m<2 = 23

Step-by-step explanation:

3*9 - 4 = 23

23 + 157 = 180 so it is correct.

180 - 23 = 157

Have a nice day!

Answer:

Step-by-step explanation:

54×54

Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Amount of bill = $124.72

and tip they left = 18% of $124.72

total amount is =$124.72 + $124.72*18%=$147.1696

so, each person pay= $147.1696/3=$49.056

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Answer:

[tex]l_c=5078.27ft[/tex]

Step-by-step explanation:

From the question we are told that:

Angle of inclination [tex]\angle=72 \textdegree[/tex]

Height [tex]h=4500ft[/tex]

Distance b\w cable base and mountain base [tex]d_{cm}=900ft[/tex]

Generally the equation for length of mountain base [tex]d_{mb}[/tex] is mathematically given by

 [tex]Tan\theta=\frac{h}{d_{mb}}[/tex]

 [tex]d_{mb}=\frac{h}{Tan\theta}[/tex]

 [tex]d_{mb}=\frac{4500}{Tan 72 \textdegree}[/tex]

 [tex]d_{mb}=1462.11ft[/tex]

Generally the Pythagoras equation for length of the cable [tex]l_c[/tex] is mathematically given by

[tex]l_c^2=h^2+(d_{mb}+d_{cm}^2)[/tex]

[tex]l_c^2=4500^2+(1462.11}+900}^2)[/tex]

[tex]l_c=5078.27ft[/tex]

Answer:

F 200.96 feet is traveled by the car

Answer:

G) 602.88 feet

Step-by-step explanation:

First find the circumference of the circle:

C = 2πr

If we use 3.14 for pi, we get:

C = 2*3.14(32)

C = 200.96 feet

Because the car takes 3 turns around the circle, multiply the circumference by 3 to find the total distance the car traveled:

200.96*3 = 602.88 feet

The value of linear equations are  f(x) = -17 and f(x) = -73 .

What is linear equation ?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

Equation with two variables of degree one is referred to as a linear equation with two variables. Formal expression: ax+by+c=0, where a, b, c R & a, b 0.

A)

   f (x) = -2*12 + 7

          = -24 + 7

          = -17

       f(x) = 5*-14 - 13

             = -60 -13

             = -73

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In a given study that the null hypothesis asserts the expected value of a phenomenon is 100 resulting in a 95% confidence interval reported as [98.76, 105.24], then we fail to reject the null hypothesis.

Therefore the answer is d) Fail to reject the null hypothesis.

A 95% confidence interval is a range of values that there is a 95% chance that the true value of a population parameter falls within. In this case, the 95% confidence interval is [98.76, 105.24], which includes the expected value of 100 that is stated in the null hypothesis.

Therefore, we fail to reject the null hypothesis because the data does not provide sufficient evidence to suggest that the true value of the population parameter is different from what is stated in the null hypothesis.

It's worth to mention that, Failing to reject the null hypothesis doesn't mean accepting it, it means that we don't have enough evidence to say that the parameter is different from the null hypothesis, it could be due the sample size, or other factors.

--The question is incomplete, complete question is as follows--

"Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 100. A research study results in a 95% confidence interval reported as [98.76, 105.24]. What decision would you make based on this confidence interval?

a) A decision cannot be made on a confidence interval; a hypothesis test is required.

b) Retain the null hypothesis.

c) Reject the null hypothesis.

d) Fail to reject the null hypothesis."

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Answer:

i dont really know answers sorry just bored lol

Answer:

yes they do

Step-by-step explanation:

both equal 1/3

8/24 = 1/3

5/15 = 1/3

1/3 = 1/3

Answer:

No, the ratios won't

Step-by-step explanation:

8/25  and 5/15.

they have Similarities, but no proportions.

have a good day!

Here is your Answer !!!

HOPE IT HELPS :)

Answer:

1  37/120

Step-by-step explanation:

Answer:

democratic leader i think im not sure tho

Answer:

an absolute dictator

Step-by-step explanation:

Answer:

x > 3

Step-by-step explanation:

This is based on the concept 'when a negative number is multiplied to both sides of the inequality, the sign gets reversed. For example, x > - 2 when it is multiplied by - 1, it becomes - x < 2.'

*only when the number is -ve.

Similarly, in this question, multiply both sides by - 1.

2x > 6

x > 6/2

x > 3

For more : take - 5 > - 2, as you know

Note that 5 is actually greater than 2. To make this true we change signs

Answer:

Here are a few of the factor pairs. The rest you can find in the pdf below.

Based on the two-way table, there seems to be a relationship between the type of books Julia's friends like best and the number of books they have read this month, A. Yes, because those who like fiction read one book at a rate four times that of those who read non-fiction books.

A two-way table, also called a contingency table, is a statistical table that shows the observed frequency for two variables.

The rows of a two-way table indicate one category and the columns indicate the other category.

For instance, based on the two-way table, one can observe that 80% of Julia's friends prefer fiction while 20% prefer non-fiction.

Among those who read 1 book this month, 80% read fiction against 20% who read non-fiction.  Similarly, among those who read 2 books this month, the same 80% read fiction against 20% who read non-fiction.

The number of students who prefer fiction = 60

The number of students who prefer non-fiction = 15

The number of fiction-preferring students who read 1 book this month = 40, which is 80% of the total (40/50 x 100).

The number of fiction-preferring students who read 2 books this month = 20, which is 80% of the total (20/25 x 100).

Thus, we can conclude that Option A is correct.

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The Two-way Table:

                                       Read 1 book         Read 2 books     Total

Prefer fiction books               40                            20              60

Prefer non-fiction books        10                              5               15

Total                                       50                            25              75

Answer:

Step-by-step explanation:

Use below formula and find the missing probability:

Answer:

f(8) = -68

Step-by-step explanation:

f(x) = -x² - 2x + 12

f(8) = ?

We just need to put 8 in for the x and solve it

f(8) = -(8)^2 -2(8) + 12

f(8) = -64 -16 +12

f(8) = -80 + 12

f(8) = -68

Answer:

The answer to the proportion is 45:25.

Step-by-step explanation:

To solve this proportion, we can use cross multiplication. That is, we can multiply the numerator of the first ratio (45) by the denominator of the second ratio (10) and the numerator of the second ratio (50) by the denominator of the first ratio (?). This will give us

45 x 10 = 500 and 50 x ? = 500.

If we divide both sides of the equation by 50, we get

? = 25.

Therefore, the answer to the proportion is 45:25.

that would be 33 square feet!!!

Answer:

=

6

3

+

5

Step-by-step explanation:

the asnwer is x=63x+5

Answer:

add the 5+5 =10

Step-by-step explanation:

5+5=10

hope that helps

The probability that the red die shows an even number or the green die shows an even number is 3/4

The sample space of a die is:

S = {1,2,3,4,5,6}

There are 3 even numbers in the above sample space

This means that the probability that a die shows an even face is:

P(Even) = 3/6 = 1/2

So, we have:

P(Even Red) = 1/2

P(Even Green) = 1/2

The required probability is then calculated as:

P = P(Even Red) + P(Odd Red) - (P(Even Red) * P(Odd Red))

This gives

P = 1/2 + 1/2 - 1/2 * 1/2

Evaluate

P = 3/4

Hence, the probability is 3/4

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None of the listed methods are used for enumerating sample points in a multiple-step experiment. So, option D is the correct answer.

Graphical methods are important mathematical tools that are very helpful when it comes to managing a vast amount of data. These also help when we need to visually represent data. These methods help quite a lot since they make it easier to keep track of data and understand it as well.

A bar chart and a histogram are similar tools that are used to represent data by plotting them as rectangular bars. These can be either vertical or horizontal. A pie chart is also a tool that uses a shape for data visualization. In its case, it represents data in the shape of a circle and all categories/data sets have their slices. So, this means that these three are not methods that can be used for enumerating sample points in a multiple-step experiment. Hence, option D is the correct option.

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[tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors of the quadratic expression.

2x^2 + 5x + 12

Consider given quadratic expression.

2x^2 + 5x + 12

Let f(x) = 2x^2 + 5x + 12

Assume f(x) = 0

2x^2 + 5x + 12 = 0

using the Quadratic Formula where

a = 2, b = 5, and c = 12

[tex]x = \frac{-b\pm \sqrt{b^2 - 4ac} }{2a} \\\\\\x = \frac{-5\pm \sqrt{5^2 - 4(2)(12)} }{2\times2} \\\\\\x = \frac{-5\pm \sqrt{25 - 96} }{4} \\\\\\x = \frac{-5\pm \sqrt{-71} }{4}[/tex]

The discriminant b^2 - 4ac < 0.

So, there are two complex roots.

[tex]x = \frac{-5\pm71i }{4}[/tex]

This means, [tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors.

2x^2 + 5x + 12

=  [tex](x- (\frac{-5+71i }{4}))[/tex] × [tex](x- (\frac{-5-71i }{4}))[/tex]

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